Methods, systems, and computer readable media for monitored application of mechanical force to samples using acoustic energy and mechanical parameter value extraction using mechanical response models

ABSTRACT

The subject matter described herein includes methods, systems, and computer readable media for monitored application of mechanical force to samples using acoustic energy and mechanical parameter value extraction using mechanical response models. One aspect of the subject matter described herein includes a method for determining mechanical property parameters of a sample. The method includes applying acoustic energy to a sample to apply a mechanical force to the sample. The method further includes measuring a response by the sample during the application of the acoustic energy to determine a value for a first mechanical property parameter of the sample. The method further includes measuring a recovery response of the sample following cessation of the application of the acoustic energy to determine a value for at least one second mechanical property parameter of the sample. The method further includes determining a value for at least one additional mechanical property parameter of the sample based on a mathematical relationship between the first, at least one second, and at least one additional mechanical property parameter.

PRIORITY CLAIM

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 61/109,102, filed Oct. 28, 2008, the disclosure ofwhich is incorporated herein by reference in its entirety.

TECHNICAL FIELD

The subject matter disclosed herein relates generally to methods fordetermining mechanical properties of materials. More particularly, thesubject matter described herein relates to methods, systems, andcomputer readable media for monitored application of mechanical force tosamples using acoustic energy and mechanical parameter value extractionusing mechanical response models.

BACKGROUND

Ultrasonic techniques for the mechanical characterization ofviscoelastic materials such as soft tissue have grown in interest due totheir clinical relevance to monitoring the progression of variousdiseases [1]. These techniques include ultrasound elastographymonitoring of strain in response to both extrinsic and intrinsic forces.Several researchers have developed elastography methods to render imagesof local strains by applying a relatively uniform, external compressionto tissue and tracking subsequent tissue displacements [2]-[16]. Theelastic modulus of tissue can be estimated using these methods withminimal complexity, providing an intrinsic measurement of the tissue'smaterial properties. However, because direct compression of tissue isrequired, elastography can be challenging when attempting to accesstissue superficial to boundaries such as organ or vascular layers.Elastographic methods that monitor tissue response to intrinsic forces,such as cardiac pulsation have also been developed but with smallstrains associated with poor contrast in parametric images [17]-[19].

One possible alternative method that has been explored involves trackinglocal strains in tissue through acoustic radiation force imaging. Ratherthan relying on external compression, acoustic radiation force methodsuse high-intensity ultrasound pulses to transfer momentum to tissue[20]-[31]. By direct application of focused radiation force at the pointof interest, these methods allow for measurement of tissue responsessuperficial to boundary layers. Several techniques involve monitoringthe dynamic response of tissue to impulsive radiation force. In acousticradiation force impulse (ARFI) imaging, tissue displacements aregenerally tracked axially after the transmission of a temporally short(e.g., <1 ms), focused acoustic radiation force excitation. Resultingtissue displacement data are typically illustrated through a set ofparametric images that include peak displacement and time to recovery.Although these parameters have been shown to be inversely related to theYoung's modulus in homogeneous elastic media [30], only the relativestiffness or compliance of tissue can be assessed from ARFI imagingbecause the magnitude of radiation force is generally unknown. Thatbeing said, the generation of impulsive tissue excitation also resultsin the initiation of shear wave propagation traveling perpendicular tothe applied force. Shear wave elasticity imaging (SWEI) producesforce-independent images of the reconstructed shear moduli of tissue bymonitoring shear wave speed [28], [32].

Other applications of acoustic radiation force imaging includemonitoring of the resonant response to excitation as invibro-acoustography [20] or harmonic motion imaging [24]. In kineticacoustic vitroretinal examination (KAVE) as developed by Walker et al.[22], [23], multiple acoustic pulses per lateral location are generatedwith a single element piston transducer to observe the steady-stateresponse of tissue to acoustic radiation force. Assuming that theforcing function is a temporal step function and tissue can be describeddiscretely as a Voigt model, images can be generated of force-freeparameters depicting the time constant, damping ratio, and naturalfrequency of the examined homogeneous tissue mimicking material.

Although these techniques can be useful in identifying certaincharacteristics of the tissue, most of the results obtained arequalitative rather than quantitative. For example, using existingultrasound measurement techniques, elasticity and viscosity of a samplecan be determined relative to that of other samples, and not in absolutenumbers. Accordingly, in light of these difficulties with associatedwith conventional acoustic radiation force measurement techniques, thereexists a need for improved methods, systems, and computer readable mediafor monitored application of mechanical force to samples using acousticenergy and mechanical parameter value extraction using mechanicalresponse models.

SUMMARY

The subject matter described herein includes methods, systems, andcomputer readable media for monitored application of mechanical force tosamples using acoustic energy and mechanical parameter value extractionusing mechanical response models. One aspect of the subject matterdescribed herein includes a method for determining mechanical propertyparameters of a sample. The method includes applying acoustic energy toa sample to apply a mechanical force to the sample. The method furtherincludes measuring a response by the sample during the application ofthe acoustic energy to determine a value for a first mechanical propertyparameter of the sample. The method further includes measuring arecovery response of the sample following cessation of the applicationof the acoustic energy to determine a value for at least one secondmechanical property parameter of the sample. The method further includesdetermining a value for at least one additional mechanical propertyparameter of the sample based on a mathematical relationship between thefirst, at least one second, and at least one additional mechanicalproperty parameters.

Another aspect of the subject matter described herein includes a methodfor quantifying at least one mechanical property parameter of a sample.The method includes applying acoustic energy to a sample and measuringresulting displacements of the sample and timings of the displacements.The method further includes modeling mechanical properties of the sampleusing a mathematical model of a mechanical response of the sample toapplied force, the model including parameters for the mechanicalproperties of the sample. The model models a steady state response ofthe sample during application of the acoustic energy and a recoveryresponse that occurs after cessation of the application of the acousticenergy. The method further includes determining, using the model, themeasured displacements, and the measured timings, quantitative valuesfor at least one of the parameters in the model.

Yet another aspect of the subject matter described herein includes asystem for determining at least one mechanical property of a sample. Thesystem includes an acoustic monitor and an acoustic transducer forapplying acoustic energy to a sample to apply mechanical force to thesample and for measuring displacements of the sample resulting from theapplication of the acoustic energy and timings of the displacements. Thesystem further includes a mechanical properties estimator for using amodel to model a mechanical response of the sample to applied force,wherein the model models a steady state response of the sample duringapplication of the acoustic energy and a recovery response that occursafter cessation of the application of the acoustic energy, and fordetermining a quantitative value for at least one of the mechanicalproperty parameters of the model using the displacements and the timingsof the displacements.

In another aspect, a computer readable medium having stored thereonexecutable instructions is provided. The instructions, when executed bythe processor of a computer, control the computer to perform steps. Thesteps include receiving radio frequency data resulting from applicationof acoustic energy to a sample. The steps further include modeling amechanical response of the sample to an applied mechanical force using amodel including a plurality of mechanical property parameters, whereinthe model models a steady state response of the sample duringapplication of the acoustic energy and a recovery response that occursafter cessation of the application of the acoustic energy, anddetermining a quantitative value for at least one of the parametersusing the model, the displacements, and the timings of thedisplacements.

As indicated in the preceding paragraph, the subject matter describedherein can be implemented using a computer readable medium having storedthereon executable instructions that when executed by the processor of acomputer control the computer to perform steps. Exemplary computerreadable media suitable for implementing the subject matter describedherein may include chip memory devices, disk memory devices,programmable logic devices, and application specific integratedcircuits. In addition, a computer readable medium that implements thesubject matter described herein may be located on a single device orcomputing platform or may be distributed across multiple devices orcomputing platforms.

Although some of the aspects of the subject matter disclosed herein havebeen stated hereinabove, and which are achieved in whole or in part bythe presently disclosed subject matter, other aspects will becomeevident as the description proceeds when taken in connection with theaccompanying drawings as best described hereinbelow.

BRIEF DESCRIPTION OF THE DRAWINGS

The features and advantages of the present subject matter will be morereadily understood from the following detailed description which shouldbe read in conjunction with the accompanying drawings that are givenmerely by way of explanatory and non-limiting example, and in which:

FIG. 1A is a schematic of a Voigt model for use by the systems andmethods according to embodiments of the presently disclosed subjectmatter;

FIG. 1B is a time-domain linear systems block diagram associated withthe Voigt model shown in FIG. 1A;

FIG. 1C is a graphical illustration of a forcing function input andresulting viscoelastic response associated with the Voigt model shown inFIG. 1A;

FIG. 2A is a schematic of a standard linear viscoelasticity model foruse by the systems and methods according to embodiments of the presentlydisclosed subject matter;

FIG. 2B is a time-domain linear systems block diagram associated withthe standard linear model shown in FIG. 2A;

FIG. 2C is a graphical illustration of a forcing function input andresulting viscoelastic response associated with the standard linearmodel shown in FIG. 2A;

FIG. 3A is a schematic diagram of an exemplary experimental setup formonitored steady-state excitation and recovery (MSSER) and SWEI imagingaccording to an embodiment of the presently disclosed subject matter;

FIG. 3B is graph of exemplary excitation and reference pulse sequencesutilized in the region of acoustic excitation for MSSER imagingaccording to an embodiment of the presently disclosed subject matter;

FIG. 3C is a graph illustrating the absence of excitation and referencepulses outside of the region of acoustic excitation for MSSER imagingaccording to an embodiment of the present disclosed subject matter;

FIG. 3D is a graph of an exemplary excitation or pushing pulse used inthe region of acoustic excitation for SWEI imaging according to anembodiment of the presently disclosed subject matter;

FIG. 3E is a graph of an exemplary reference pulse sequence used outsidethe region of acoustic excitation for SWEI imaging according to anembodiment of the presently disclosed subject matter;

FIGS. 4A through 4D are representative displacement profiles with fittedmodel for gelatin phantoms of different elastic modulus values from6-cycle, 8-cycle, 10-cycle, and 12-cycle MSSER imaging beam sequences,respectively;

FIG. 5 is a graph of estimated stress versus estimated strain values forgelatin phantom materials with linear fits;

FIG. 6 is a graph of the measured elastic modulus values from uniaxialcompression and estimated stress versus estimated strain data from MSSERimaging for gelatin phantom materials;

FIG. 7 is a graph of correlation coefficients±standard deviationcompared with elastic modulus for gelatin phantom material displacementprofile data fitted to the Voigt model;

FIG. 8 illustrates parametric images of homogeneous gelatin phantommaterials from SWEI and a combined SWEI and MSSER approach according toan embodiment of the presently disclosed subject matter;

FIGS. 9A through 9D are graphs of parameters of the Voigt modelcalculated from SWEI measures of elastic modulus and MSSER displacementprofiles over a 2.5 mm range directly above the imaging focus forgelatin phantom samples according to an embodiment of the presentlydisclosed subject matter;

FIG. 10 is a graph illustrating representative displacement profileswith fitted standard linear model for excised pig muscle sample fromdifferent pushing pulse MSSER beam sequences according to embodiments ofthe presently disclosed subject matter;

FIGS. 11A through 11I illustrate parametric images of excised pig musclefrom B-mode, conventional ARFI, SWEI, and a combined SWEI and MSSERapproach;

FIG. 12 is a block diagram of an exemplary system for determiningmechanical properties of a sample according to an embodiment of thepresently disclosed subject matter; and

FIG. 13 is a flow chart illustrating an exemplary process fordetermining mechanical properties of a sample from radio frequency (RF)data resulting from application of acoustic energy to the sampleaccording to an embodiment of the presently disclosed subject matter.

DETAILED DESCRIPTION Overview

The subject matter described herein includes methods, systems, andcomputer readable media for monitored application of mechanical force tosamples using acoustic energy and mechanical parameter value extractionusing mechanical response models. In one exemplary implementation acombined approach to radiation force imaging can be used. The combinedapproach includes measuring the tissue response to steady state acousticforce excitation and the tissue response after cessation of theexcitation. The subject matter described herein includes modeling theviscoelastic tissue response to radiation force excitation discretelythrough the application of the Voigt and standard linear models anddetermining model parameter values using measured tissue responsevalues. In addition, although the subject matter disclosed herein isdisclosed primarily with a focus on viscoelastic materials, it is to beunderstood that the principles described can be applied to determine themechanical parameter values for any material that can be accuratelymodeled using a mechanical model that models the mechanical response ofthe material when excited by a forcing function and whose displacementsettles to an equilibrium value under application of the forcingfunction.

The imaging technique described herein is a noninvasive radiation forcebased method using a commercially available ultrasound scanner andlinear array transducer to monitor steady-state tissue response duringextended force application and also the transient or recovery responsefollowing cessation of force application. In this way, the presenttechnique mimics a materials creep test by applying a constant loadwhile observing the material “creep” or slow movement to steady statedisplacement but then also observing the transient response after forcetermination. This combined imaging technique is referred to herein asmonitored steady-state excitation and recovery (MSSER) imaging. Theimaging technique is described below first to obtain an estimate ofYoung's modulus to confirm that MSSER imaging approximates viscoelastictissue response to uniaxial mechanical compression. It will then bedemonstrated that the radiation force imaging methods described herein,in conjunction with SWEI, discern all parameters of the viscoelasticmodel in quantitative terms or numeric values. The numeric valuesdetermined for the parameters in the experiments described herein arenot in terms of the applied radiation force magnitude. Experimental dataare collected in homogeneous gelatin phantoms of different stiffness andin excised pig muscle.

Viscoelastic Models

The mechanical properties of viscoelastic materials, particularly softtissue, have been widely studied in the field of biomechanics withseveral viscoelastic models describing material response to externalmechanical stimuli [33]. Two such models that predict a similarmechanical response to a constant stress application are the Voigt andstandard linear models. Either model can serve as a viable predictor ofresponse of a material sample to acoustic radiation force excitation.For instance, referring to FIG. 1(A, a schematic of the mechanical modelfor the Voigt model is provided, the model consisting of a linear springwith spring constant μ in parallel with a dashpot with coefficient ofviscosity, η. The linear spring produces instantaneous displacementproportional to the applied force while the dashpot produces velocityproportional to the applied force. Therefore, if an applied force Factson the linear spring to produce an instantaneous displacement x(0) then,F=μx(0). Similarly, if the same applied force acts on a dashpot, theresult will be a velocity through time t so that F=η(dx(t)/dt). Thedifferential equation describing the Voigt model is as follows:

$\begin{matrix}{{F(t)} = {{E_{\mu}{x(t)}} + {E_{\mu}\tau_{\sigma}\frac{{x(t)}}{t}}}} & (1)\end{matrix}$

where F(t) [N] is the applied force, x(t) [m] is displacement, E_(μ)[N/m] is the relaxed elastic modulus, and σ_(σ) [s] is the relaxationtime constant for constant stress. The constants from Equation (1) canbe described in terms of the spring and damper constants in FIG. 1A:

$\begin{matrix}{{E_{\mu} = \mu},{\tau_{\sigma} = \frac{\eta}{\mu}}} & (2)\end{matrix}$

In FIG. 1B, a time-domain linear systems block diagram of the Voigtmodel is illustrated, where force F(t) is the input, the system impulseresponse is listed inside the box, and displacement through time x(t) isthe output. In addition, a graphical representation of the input forcingfunction and subsequent viscoelastic response is illustrated in FIG. 1Cin the instance where ξ is sufficiently large so that the responseapproaches the steady-state value A/E_(μ). If the forcing function forthis model is described as a temporal unit step function U(t) of forcemagnitude A [N] from time zero to ξ, the Voigt output given themechanical properties E_(μ) and τ_(σ) of the sample predicts anexponential behavior with time constant τ_(σ), and a steady-statedisplacement in creep loading, x_(ss) achieving the followingrelationship:

$\begin{matrix}{{{x(t)} = {\frac{A}{E_{\mu}}( {1 - ^{- \frac{t}{\tau\sigma}}} )}};{{{for}\mspace{14mu} 0} < t < \xi}} & (3) \\{x_{ss} = \frac{A}{E_{\mu}}} & (4)\end{matrix}$

In FIG. 2A, a schematic of the linear spring, dashpot system governingthe standard linear model is illustrated. The standard linear model isalso referred to as the Kelvin model. In this model, there is anadditional linear spring in series with the dashpot, which accounts foran immediate initial deflection in displacement in response to forceexcitation. The differential equation describing the Standard Linearmodel is as follows:

$\begin{matrix}{{F(t)} = {{\tau_{ɛ}\frac{F(t)}{dt}} = {E_{\mu}( {{x(t)} + {\tau_{\sigma}\frac{x(t)}{dt}}} )}}} & (5)\end{matrix}$

where τ_(ε) [s] is the relaxation time constant for constant strain. Thematerial constants from Equation (5) can be defined in terms of thespring, damper system from FIG. 2A:

$\begin{matrix}{{E_{\mu} = \mu_{0}},{\tau_{\sigma} = {\frac{\eta_{1}}{\mu_{0}}( {1 + \frac{\mu_{0}}{\mu_{1}}} )}},{\tau_{ɛ} = \frac{\eta_{1}}{\mu_{1}}}} & (6)\end{matrix}$

Considering a temporal unit step forcing function input, the time-domainlinear-systems block diagram for the standard linear model isillustrated in FIG. 2B along with a graphical representation of theinput and viscoelastic response in FIG. 2C:

$\begin{matrix}{{{x(t)} = {\frac{A}{E_{\mu}} - {\frac{A( {\tau_{\sigma} - \tau_{ɛ}} )}{E_{\mu}\tau_{\sigma}}^{- \frac{t}{\tau\sigma}}}}};{{{for}\mspace{14mu} 0} < t < \xi}} & (7)\end{matrix}$

The illustration in FIG. 2C depicts the instance where is sufficientlylarge so that the response approaches the steady-state value A/E_(μ). Itis noted that both the standard linear and Voigt models share the samerelaxation time constant for constant stress τ_(σ) and the samesteady-state response as described in Equation (4). There are twoprimary differences between the impulse responses and displacementspredicted by the Voigt and standard linear models. First, the standardlinear model incorporates an additional relaxation time constant forconstant strain. τ_(ε), into the model, which is not required by theVoigt model. Second, while the Voigt model predicts zero instantaneousdisplacement, the standard linear model predicts an instantaneousdeflection with force application, and the amount of deflection isdetermined by the mechanical properties of the sample:

$\begin{matrix}{{x(0)} = \frac{A\; \tau_{ɛ}}{E_{\mu}\tau_{\sigma}}} & (8)\end{matrix}$

By developing an acoustic radiation force technique to mimic theconstant temporal unit step stress inputs shown in FIG. 1 or FIG. 2, andassuming that the sample of interest is composed of a viscoelasticmaterial, the displacement solutions to either system can be modeled andmaterial parameters of interest can be extracted from the model. As willbe described in more detail below, the applied radiation forcemagnitude, A, can be determined from the elastic modulus E and MSSERdata. The mechanical properties of interest can then be determined inquantitative terms (i.e., numeric values). A is related to the magnitudeof radiation force per unit volume (the body force magnitude), |{rightarrow over (F)}|[N/m³], by the following relationship:

A=|{right arrow over (F)}|×L _(Lat) ×L _(Elev) ×L _(Axial)  (9)

where L_(Lat) [m], L_(Elev) [m], and L_(Axial) [m] are the lateral,elevational, and axial spans over which the acoustic radiation bodyforce acts. |{right arrow over (F)}| has been described [31], [34] as:

$\begin{matrix}{{\overset{arrow}{F}} = \frac{2\alpha \; I}{c}} & (10)\end{matrix}$

where c [m/s] is the speed of sound, α [Np/m] is the absorptioncoefficient of the media, and I [W/m²] is the temporal average intensityat a given spatial location. Variations in α and c from sample to sampleand even within a single sample structure yield uncertainty in deliveredbody force magnitude and, therefore, in A. One approach to approximatingA is to measure α, c, and I directly to estimate |{right arrow over(F)}| by using Equation (10). However, this approach is generally notclinically relevant. An alternative approach is to measure the elasticmodulus (e.g., Young's modulus) of the material sample E [N/m²] by SWEIto estimate A using Equations (9) and (14).

First, regarding the approach that involves approximating E from anestimated body force magnitude, |{right arrow over (F)}|, the elasticmodulus E [N/m²] of a viscoelastic material sample at equilibriumdeformation can be determined by the slope of its stress versus strainrelationship:

$\begin{matrix}{E = \frac{\Delta \; \sigma}{\Delta \; ɛ}} & (11)\end{matrix}$

where σ [N/m²] is the applied stress and ε is a unitless measure of theresulting strain. To estimate the elastic modulus in Equation (11), themagnitude of radiation force |{right arrow over (F)}|[N/m³] is adaptedto units of stress [N/m²] while steady state displacement χ_(ss) [m] isadapted to unitless strain. The estimated stress σ [N/m²] can beapproximated as the magnitude of the radiation body force multiplied bythe axial length L_(Axial) [m] over which the body force acts. Estimatedstress represents the applied force per area spanning the lateral andelevational dimensions:

{tilde over (σ)}=|{right arrow over (F)}|×L _(Axial)  (12)

Similarly, the estimated strain {tilde over (ε)} can be defined as thesteady state displacement normalized by the original axial length L₀ [m]of material over which the body force acts:

$\begin{matrix}{\overset{\sim}{ɛ} = \frac{{\overset{\sim}{x}}_{ss}}{L_{0}}} & (13)\end{matrix}$

By substituting Equations (12) and (13) into Equation (11) andintroducing a correction factor C, an estimated elastic modulus {tildeover (E)} [N/m²] can be calculated:

$\begin{matrix}{\overset{\sim}{E} = {{\frac{\Delta \; \overset{\sim}{\sigma}}{\Delta \; \overset{\sim}{ɛ}} \times C} = {\frac{\Delta( {{\overset{arrow}{F}}L_{Axial}L_{0}} )}{\Delta \; x_{ss}} \times C}}} & (14)\end{matrix}$

where Δ{tilde over (σ)}/Δ{tilde over (ε)} is the slope of estimatedstress versus estimated strain. The correction factor C is predominantlyimplemented because of system-dependent factors that lead tounderestimation of steady-state displacement as well as error inestimation of L_(Axial) and L₀. These factors contributing to Careaddressed more specifically hereinbelow. Note that the correction factorcan be globally determined, and its established value can be usedconsistently across all samples.

Second, regarding the case of the elastic modulus being determined bySWEI, Equation (14) can be used to measure an estimated body forcemagnitude, |{right arrow over (F)}|. This estimated body force magnitudecan then be related back to A in discrete viscoelastic models throughEquation (9). That is, the applied radiation force magnitude for atissue sample can be calculated by multiplying the estimated body forceby the dimensions over which the force is applied using Equation (9).Once the value for A is determined in this way, values for additionalmechanical properties can be determined based on the relationshipsbetween those mechanical properties and the applied force magnitude(See, e.g., Equations (3) through (8) above). As a result, themechanical properties of the tissue sample can be described in absoluterather than comparative terms.

Methods A. Radiation Force Imaging

In the experiments described herein, a Siemens SONOLINE Antaresultrasound scanner produced by Siemens Medical Solutions USA, Inc.,Ultrasound Division, with a VF7-3 transducer was used. Imaging wasperformed at an axial focal distance of 20 mm with an F/1.5 focalconfiguration. Similar to conventional ARFI imaging, MSSER used twotypes of beams that included higher intensity 6-, 8-, 10-, or 12-cyclepushing beams and conventional two-cycle B-mode tracking beams. Tworeference-tracking beams were fired first to establish initial position.The reference tracking beams were then followed by a sequence of 30pushing beams interspersed with single-tracking beams, which served tomonitor displacement during force application. This single push-singletrack sequence was implemented to mimic a temporal unit step forcingfunction while still allowing for displacement tracking throughout thepushing period. Finally, 60 additional tracking beams followed forcecessation monitored displacement relaxation. FIG. 3A is a schematicdiagram illustrating a sample and lateral ranges over which pushing andtracking beams were applied. In FIG. 3A, sample 300 represents asectional slice of a sample being imaged by an ultrasound transducer302. The region of acoustic excitation by ultrasound transducer 302 isillustrated by location L₀. The regions L₁-L_(N) and L₁-L_(N) arelocations lateral to the region of acoustic excitation. As illustratedin FIGS. 3B and 3C, MSSER imaging involves excitation with pushingpulses (represented by the taller arrows) and reference pulses(represented by the shorter arrows) in the region of acoustic excitationL₀ and no reference pulses outside the region of acoustic excitation. Itshould be noted that the region of acoustic excitation L₀, althoughshown in the center of sample 300 in FIG. 3A, can be at any location inthe sample.

Tracking and pushing beams were administered at center frequencies of6.15 MHz and 4.21 MHz, respectively. The pulse repetition frequency(PRF) for the technique was 6.65 kHz for pushing pulses and 7.39 kHz fortracking pulses. The total duration of the pushing sequence in thisconfiguration, including intermittent tracking beams, was 8.6 ms, andthe total data acquisition time in each lateral position was 17.0 ms.Radiation force-induced displacement was monitored in 20 laterallocations spaced 0.53 mm apart and spanning a total lateral field ofview (FOV) of 10.6 mm. The image acquisition time for the entire fieldof view under these operating parameters was 0.339 s.

Four different pushing beams were used for MSSER imaging during separateimage acquisitions, including 6-cycle (1.4 μs), 8-cycle (1.9 μs),10-cycle (2.4 μs), and 12-cycle (2.9 μs) pulses. By increasing the pulselength of pushing beams, the effective magnitude of the mimickedtemporal unit step forcing function was increased. In this way, MSSERimaging allowed control of the magnitude of force application A [N]through pushing pulses of variable duration. Similarly, it is possibleto vary the duration of force application by varying the total number ofpushing pulses. In the experiments described herein, 30 pushing pulsesper lateral location were consistently used. Axial displacements werecalculated using the acquired tracking lines and conventionalone-dimensional cross correlation.

SWEI was performed using the same transducer, focal configuration, axialfocus, frequencies, and number of lateral locations. The distancebetween lateral locations was 1.06 mm, twice that of MSSER. The SWEIbeam sequence fired two reference tracking pulses, one 300-cycle (52 μs)pushing pulse, and then 123 tracking pulses to monitor induceddisplacements in positions lateral to the region of radiation forceexcitation. FIGS. 3D and 3E illustrate exemplary excitation andreference pulses used for SWEI imaging. In FIG. 3D, it can be seen thatin SWEI imaging, only the pushing pulse occurs at location L₀. From FIG.3E, the reference pulses occur at locations lateral to location L₀.Unlike conventional ARFI imaging beam sequences, the SWEI pushing pulselocation remained stationary while tracking locations were translatedacross the FOV. The same one-dimensional cross-correlation methods wereused to calculate axial displacements. At each spatial location in theFOV, a shear wave velocity was calculated as lateral distance from theexcitation focus divided by time to peak displacement. Assuming alinear, elastic solid and constant density, the shear wave speed (c_(T))can be related to Poisson's ratio (v), density (ρ), and elastic modulus(E) [31]:

$\begin{matrix}{c_{T} = \sqrt{\frac{E}{2( {1 + v} )\rho}}} & (15)\end{matrix}$

Conventional ARFI imaging was performed with generally the same imagingparameters as for SWEI. The number of lateral locations was increased to40, while lateral spacing for conventional ARFI was 0.531 or half of thelateral spacing for SWEI. Conventional ARFI sequences used two referencetracking pulses, one 300-cycle (52 μs) pushing pulse, and then 60tracking pulses.

B. Homogeneous Gelatin Phantoms

Four tissue mimicking, gelatin-based phantoms made with differentconcentrations of gelatin to vary stiffness were used to test themethods and systems described herein. Elastic modulus values resultingfrom mechanical testing for each of four gelatin samples are shown inTable I below. Methods for determining the elastic modulus values aredescribed below. MSSER imaging was performed on each gelatin sample withseparate acquisitions using 6-cycle, 8-cycle, 10-cycle, or 12-cyclepushing pulses.

TABLE I Measured Elastic Modulus Values from Mechanical Testing forDifferent Homogeneous Gelatin Phantom Materials Elastic Gelatin ModulusPhantom (kPa) Sample A 18.7 ± 0.4 Sample B 13.6 ± 0.4 Sample C 10.6 ±0.3 Sample D  4.7 ± 0.1

To implement the first approach to approximating E (by estimating c, α,and I to calculate |{right arrow over (F)}|), speeds of sound andattenuation coefficients in the phantoms were measured. The measuredvalues agreed with published values [35], [36]. Because nonlinearpropagation of MSSER pushing pulses in water did not allow measurementof the acoustic intensity directly, measures of temporal averagedintensity were made using the comparison method described in Palmeri etal. [31]. I_(SPTA) of low amplitude MSSER imaging pulses was measuredwith an Onda HGL-0200 hydrophone produced by Onda Corporation,Sunnyvale, Calif. Displacements at the focus of a compliant gelatinphantom were then observed for low- and high-power radiation forceapplication. By assuming a linear relationship between intensity anddisplacement, the ratio of the displacements from high-power tolow-power settings represented the ratio of I_(SPTA) between high-powerand low-power settings. Using the speed of sound, attenuation, andintensity measurements, the force magnitude for each pushing pulse inthe gelatin phantoms was estimated. Equation (12) was then used totranslate estimated body force magnitude to units of estimated stress{tilde over (σ)}. The axial length over which the body force actsL_(Axial) [m] from Equation (12) was estimated as the −6 dB (full widthat half maximum) (FWHM) width of the MSSER pushing pulse.

To implement the second approach of approximating A discussed above froman independent estimate of the elastic modulus, SWEI was performedimmediately after MSSER data acquisition without moving the transducerwith respect to the sample. The resulting displacement profiles fromradiation force imaging were fit to the Voigt function (Equation (3)),which was defined in custom MATLAB (Mathworks Inc., Natick, Mass.) code.In particular, the fitting between the model function and actual datawas performed using MATLAB function ‘fminsearch’. Parameter values wereextracted directly from the output of the ‘fminsearch’ function.

To estimate strain from Equation (13) for a given MSSER acquisition, thesteady-state displacement of the average representative displacementprofile was measured. Representative displacement profiles weredisplacement profiles with a correlation coefficient greater than 0.975to the nonlinear least squares fit to the Voigt model and were locatedwithin an axial region directly above the focus (e.g., a 2.5 mm region).The original length of tissue that was displaced by radiation forceexcitation L₀ was estimated as the FWHM width of the force distributionacross the axial range in all samples. Equations (14) and (9) were thenused to estimate A.

Within 24 hours of ARFI and SWEI imaging, the gelatin phantoms weremechanically tested using a BOSE EnduraTEC ELF 3200 produced by BOSECorporation, ElectroForce Systems Groups, Eden Prairie, Minn. toquantify the elastic modulus of the samples (Table I). The load framewas fitted with a 225 N load cell and stainless steel axial compressionplatens. The force resolution for the load cell was 0.01 N. Cylindricalphantoms approximately 20 mm in diameter and 10 mm in height were placedbetween the stainless steel plates and coated with mineral oil to allowfor unconfined and approximately frictionless compression. Strains up to15% were achieved at strain rates of less than 1.0% per second. Thismechanical testing was performed at slightly slower strain rates thanthose estimated from MSSER (greater than 1.5% per second) to ensure thatsteady-state displacement was reached between incremental levels ofcompressive force. A linear least-squares regression was performed onthe stress versus strain profiles, and the slope of the regressionindicated the elastic modulus of each material sample.

Each material sample was then associated with a measured elastic modulusE, and an estimated stress versus estimated strain was determined fromMSSER. The correction coefficient C was determined using MSSER data fromall gelatin samples simultaneously by fitting a least-squares linearregression of E versus Δ{tilde over (σ)}/Δ{tilde over (ε)} anddetermining the slope with a y-intercept value of zero. Using Equation(14), estimated elastic modulus {tilde over (E)} values were determined.Similarly, by spatially registering SWEI measures of E to MSSER data,Equations (14) and (9) were used to estimate force magnitude, A. Otherviscoelastic parameters were determined by fitting MSSER data to theVoigt model described by Equation (3), and parametric images wererendered. It is noted that although this approach discloses fitting thedisplacement profiles to the Voigt function, this approach can be usedto fit the collected date with other material models (e.g., the standardlinear model).

C. Excised Pig Muscle

In another experimental example, an excised pig muscle sample was imagedusing 6-cycle, 8-cycle, 10-cycle, and 12-cycle pushing pulse MSSER. SWEIand conventional ARFI imaging were also performed without moving thetransducer with respect to the sample. The speed of sound andattenuation were assumed to be consistent with typical values for humantissue at 1540 m/s and 0.3 dB/cm/MHz, respectively. The mechanicaltesting, slope of the estimated stress versus estimated strain curve,and determination of the elastic modulus for the tissue sample wereacquired using the same methods described above with respect to thetesting of the homogeneous gelatin phantoms. An estimated elasticmodulus {tilde over (E)} from MSSER imaging was determined usingEquation (14), and the same correction coefficient C value wasdetermined from the gelatin phantoms. Because an initial deflection wasobserved from MSSER imaging, the pig tissue sample displacement profileswere fit to the standard linear model as described in Equations (5)through (8) using the ‘fminsearch’ function in MATLAB, as describedherein above for the Voigt model.

Results A. Homogeneous Gelatin Phantoms

Representative displacement profiles from MSSER imaging are shown inFIG. 4 for acquisitions using 6-cycle (FIG. 4A), 8-cycle (FIG. 4B),10-cycle (FIG. 4C), and 12-cycle (FIG. 4D) pushing modulus valuesdescribed in Table I. Representative profiles corresponded to theaverage displacement profile within a 2.5 mm axial region directly abovethe imaging focus that had a correlation coefficient greater than 0.975to the nonlinear least squares fit of the profile to the Voigt model.The fitted model is presented as a dashed line, while representativedisplacement data from each sample are displayed in open symbols.

FIG. 5 shows the estimated stress versus estimated strain data for eachgelatin sample. Estimated stress values were calculated from Equations(10) and (12) for each of the 6-cycle, 8-cycle, 10-cycle, and 12-cycleMSSER imaging acquisitions. A linear least-squared fit is illustrated asdashed lines while estimated stress and strain data are shown as opensymbols. Estimated strains were computed from Equation (13) where thesteady-state displacement for each acquisition is taken from therepresentative profile data shown in FIG. 4.

FIG. 6 shows the elastic modulus values from mechanical testing (TableI) plotted against the slope of the least-squared fits to the estimatedstress and strain data from FIG. 5. The dashed line represents a linearleast-squared fit with y-intercept of zero while the elastic modulusdata are represented as points with standard deviation bars. The slopeof the linear least-squared fit was 0.4859 and represented the value forthe correction coefficient C in Equation (14). Using this value and theestimated stress and strain data from FIG. 5, estimated elastic modulusvalues {tilde over (E)} were calculated from Equation (14) and arereported in Table II. Also included in Table II are elastic modulusvalues determined from mechanical testing and average elastic modulusvalues determined from SWEI.

TABLE II Comparison of Elastic Modulus Values from Mechanical Testingand Radiation Force Methods Gel Enduratec E SWEI E MSSER {tilde over(E)} Phantom (kPa) (kPa) (kPa) Sample A 18.7 ± 0.4 18.4 ± 2.2  17.1 ±2.3 Sample B 13.6 ± 0.4 12.6 ± 1.3  14.7 ± 1.0 Sample C 10.6 ± 0.3 8.5 ±0.8 10.6 ± 0.3 Sample D  4.7 ± 0.1 5.5 ± 0.6  6.3 ± 0.4

Mean correlation coefficient values with standard deviations for therepresentative displacement profiles are displayed in FIG. 7. Values areplotted versus elastic modulus of the gelatin phantom samples. Theduration of MSSER pushing pulse is shown in open symbols.

In FIG. 8, parametric images of gelatin phantoms are rendered fromspatially registered SWEI and 12-cycle pushing pulse MSSER imaging datawith an imaging focus of 20 mm. Columns are labeled with theviscoelastic parameter of interest while rows have figure numbers thatinclude the name of gelatin sample. For example, the row labeled FIG. 8Acorresponds to imaging data from gelatin phantom Sample A. In the firstcolumn, elastic modulus images are depicted from SWEI data spatiallyregistered to the lateral span of MSSER imaging. As described above, thelateral span and spacing between lateral beams in SWEI were twice asmuch as in MSSER imaging. Using the SWEI measures of the elasticmodulus, the Voigt model fits to the MSSER displacement profiles, andEquations (9) and (14), parametric images of mechanical parameters areshown depicting force magnitude A [N] (second column), spring constant μ[N/m] (third column), coefficient of viscosity η [kg/s] (fourth column),and relaxation time constant for constant stress τ_(σ) [s] (fifthcolumn). It is important to note that quantitative numeric values aredetermined for the mechanical parameters. Unlike conventional techniqueswhich determine mechanical properties of samples qualitatively (e.g.,relative to those of other samples), the values computed using themethods described herein are in absolute or non-relative terms. Byperforming the curve fitting from the displacement data and estimatingthe applied force magnitude described above, the equations for theviscoelastic model can be solved for viscoelastic parameters, such aselasticity (spring constant) and viscosity coefficient.

FIGS. 9A-9D respectively illustrate average values for relaxation timeconstants for constant stress τ_(σ) [s], force magnitude A [N],coefficients of viscosity η [kg/s], and spring constants μ [N/m] as afunction of the elastic modulus and number of cycles used for pushingpulses in MSSER. Average values are shown in open symbols with errorbars representing standard deviation. Values were computed over the same2.5 mm range directly above the imaging focus as used in determiningrepresentative displacement profiles from FIG. 4.

B. Excised Pig Muscle

Representative displacement profiles from MSSER imaging of excised pigmuscle are shown in FIG. 10. Displacement data are in open symbols whilethe dashed lines represent a nonlinear least-squared fit to the StandardLinear model. As described above, the same correction coefficient Cdetermined from the gelatin samples (FIG. 6) was used to calculate anestimated elastic modulus {tilde over (E)} from the excised pig musclesample. The mechanical testing elastic modulus, SWEI average elasticmodulus, and MSSER estimated elastic modulus {tilde over (E)} are listedin Table III.

TABLE III Comparison of Elastic Modulus Values from Mechanical Testingand Radiation Force Methods Enduratec E SWEI E MSSER {tilde over (E)}Material (kPa) (kPa) (kPa) Porcine 129.3 ± 10.6 106.8 ± 18.7 122.4 ± 5.0Muscle

FIG. 11 illustrates (in FIG. 11A) a B-mode, and (in FIGS. 11B and 11C)conventional ARFI peak displacement and time to 67% recovery images ofthe excised pig tissue sample. MSSER and SWEI displacement data were fitto the standard linear model to render parametric images of (in FIG.11D) force magnitude A, (in FIG. 11E) time constant for constant stressτ_(σ), (in FIG. 11F) time constant for constant strain τ_(ε), and (inFIGS. 11G-11I) both spring constants μ₀ and μ₁ and the coefficient ofviscosity η₁.

DISCUSSION

In regard to the correction factor C in Equation (14), steady-statedisplacement underestimation, as well as errors in estimating L_(Axial)and L₀ from Equations (12) and (13), can be accounted for in theestimation of the elastic modulus. It has been observed that themagnitude of displacement underestimation can be larger than 50% for thefocal configurations and other imaging parameters used according to thesystems and methods disclosed herein, although less than 50%displacement underestimation can be expected in the steady-statecondition. In addition, discrete viscoelastic approximations do notaccount for distributed loads, which can reduce the overall displacementachieved at a given point. The FWHM of the radiation force footprint maynot accurately represent the axial span over which the applied bodyforce acts or the original length of tissue that displaces in responseto radiation force excitation. These error sources are largely systemdependent, and relative displacement underestimation can be estimated asconstant for a given applied force.

Another source of error that may affect C to a smaller extent is thecomparison method used for measuring I, which can overestimate the truefocal intensity [31], [38]. Further, there may be a small amount ofdisplacement relaxation that occurs between force cessation and theinitiation of the tracking pulse. Elastodynamic models of tissueresponse to radiation force excitation [30], [31], [37] and typicalrelaxation time constants measured in the experimental analysesdiscussed above imply a worst case of 9% displacement relaxation.Because it is known that the material samples of interest areviscoelastic rather than purely elastic, a larger delay in forcepropagation can be expected, which can result in less relaxation beforedisplacement tracking. Accordingly, C can be predominantly animaging-system-dependent parameter and can be considered consistentacross all imaging samples. In the experimental configurations discussedabove. C was determined by using a least-squared linear fit betweenmeasured elastic modulus values E and estimated stress versus estimatedstrain values Δ{tilde over (σ)}/Δ{tilde over (ε)} for each gelatinsample. The same C value is used consistently for all reported elasticmodulus estimations {tilde over (E)} and parametric images for bothgelatin and excised pig muscle samples.

Using planar wave assumptions, the magnitude of acoustic radiation forcecan be proportional to temporal average intensity, attenuation, and thespeed of sound (Equation (10)). Based on hydrophone experiments, it hasbeen found that the attenuation of the gelatin phantoms used in theexperiments discussed above was dependent primarily on the concentrationof additive graphite, which was held constant in all samples. Becausethe speed of sound and attenuation were constant in all 4 gelatinsamples, the effective magnitude of the mimicked temporal unit stepforce in MSSER imaging was proportional to the number of cycles (ortemporal duration) transmitted per pushing pulse. Data in FIG. 4depicted the response of gelatin phantom samples with different elasticmodulus values (Table I) to an increasing number of pushing pulsecycles. The Voigt model shown in dashed lines fit the displacement datawell, which indicated that the model is appropriate.

There are two trends that were apparent from this data. First, anincrease in force magnitude applied to a given gelatin sample can resultin increased steady-state displacement. This trend was apparent whendisplacement profiles from the same sample were compared from FIG. 4A(smallest force magnitude) to FIG. 4D (largest force magnitude). Second,for the same applied force magnitude, stiffer phantoms can exhibit asmaller steady-state displacement than more compliant gelatin phantoms,which was in agreement with our model at equilibrium (Equation (4)).These trends were further expressed in FIG. 5 where the force magnitudewas expressed as an estimated stress {tilde over (σ)}, and steady-statedisplacement was scaled by an original length constant L₀, to beexpressed as an estimated strain {tilde over (ε)}. As phantom stiffnessincreased, the slope of estimated stress versus estimated strain becamesteeper.

Furthermore, the slope of the least-squared linear fits in FIG. 5 cangenerally be proportional to the mechanically tested elastic modulusvalues by a constant correction factor, C. The least squared solutionfor C was calculated from the gelatin phantom data and was displayed inFIG. 6. From FIG. 6, it was evident that data points from samples A, B,and D fell either above or below the linear regression. These errorswere further reflected in Table II, where estimated elastic modulusvalues from MSSER imaging data (third column) for Samples A, B, and Ddid not exactly match the measured elastic modulus values frommechanical testing (first column). Although these values did not exactlymatch, they were generally consistent. Standard deviations for thesemeasurements overlapped for all samples except for Sample D, and maximumerror between estimated elastic modulus and measured elastic modulus was1.6 kPa. Furthermore, when comparing MSSER elastic modulus estimates tothose obtained from SWEI (column II), MSSER elastic modulus estimateswere generally comparable. Although SWEI provided substantially moreaccurate elastic modulus estimates in Samples A and D, MSSER estimateswere much more accurate in Sample C and were within 0.1 kPa of error forestimated elastic modulus for Sample B.

Equations and numerical results of the experimental configurationsdiscussed herein are based on the approximation that MSSER imagingmimics unconfined, uniaxial mechanical testing. The agreement betweenMSSER elastic modulus values and mechanical testing values suggestedthat these assumptions are appropriate in the experimental context.Furthermore, the agreement between SWEI elastic modulus values andmechanical testing values suggested that SWEI can provide an accurateestimation for this mechanical parameter and supported the use of acombined SWEI and MSSER imaging technique.

Discrepancies between estimated MSSER elastic modulus values andmeasured elastic modulus values for Sample A can be attributed to largeramounts of decorrelation in displacement estimation. Signaldecorrelation generally became more prevalent in the MSSER data withstiffer material and less force. To illustrate this claim, data in FIG.7 present the mean correlation coefficients from the representativedisplacement profiles to the Voigt model for each gelatin phantom. As aresult of larger amounts of signal decorrelation, the trend in data fromFIG. 7 showed that the correlation coefficients decreased with increasedelastic modulus and decreased force magnitude. Signal decorrelation wasalso evident in FIG. 8 where decorrelation resulted in larger amounts ofspatial discontinuity in the mechanical parameters being imaged. Thediscontinuity was much more prevalent in parametric images from stifferphantoms (row A and B) than parametric images for more compliantphantoms (row C and D).

Despite some signal decorrelation present in the data, trends inparametric images displayed in FIG. 8 agreed with expected results. Inthe first column, elastic modulus data from SWEI are presented. Asanticipated, elastic modulus values decreased from Sample A to Sample D,which was consistent with mechanical testing results. In the secondcolumn, parametric images of force magnitude were presented. It wasapparent from these images that for all samples, force magnitude washighest around the focus (20 mm) and decreased gradually with increasedaxial distance.

Furthermore, despite the apparent signal decorrelation that was presentprimarily in Sample A and Sample B, force magnitude appeared to beconstant for all samples. This visual analysis was confirmed in FIG. 9Bwhere average force magnitude was displayed for each gelatin sample. Foreach sample, the average force magnitude showed the expected trend ofincreasing force magnitude with increasing number of cycles per pushingpulse. Furthermore, for each gelatin sample, force magnitude at 12-cyclepushing pulse was roughly twice as large as force magnitude at 6-cyclepushing pulses.

The apparent increase in force magnitude for a given MSSER beam sequencefor Samples A and B was likely the result of artifacts in thesteady-state displacement values from signal decorrelation. Other trendsvisually apparent in FIG. 8 included increased spring constant valueswith increased elastic modulus, increased coefficient of viscosity withincreased elastic modulus, and stable relaxation time constant valuesacross all gelatin phantom samples. Again these trends are confirmedfrom the plots in FIG. 9. It is also apparent from FIGS. 9A, C, and Dthat standard deviation increased for the Voigt parameters withincreased elastic modulus and decreased number of cycles per pushingpulse. These trends are in agreement with the trends from correlationcoefficient data in FIG. 7.

Representative displacement profiles were depicted in FIG. 10 anddescribed the response of pig tissue to radiation force excitation. Theinitial deflection at the first time point along with the immediatedeflection following force cessation suggested that pig tissue wasbetter characterized by the Standard Linear model. Although displacementdata from MSSER were fit to the Standard Linear model rather than theVoigt model, the estimated elastic modulus values in Table III werecalculated by the same methods as described for the gelatin phantoms.The same 0.4859 value for the correction coefficient C was used tocompute the estimated elastic modulus from MSSER. As shown in Table III,the estimated elastic modulus from MSSER agreed well with themechanically tested elastic modulus values and with SWEI. Although theestimated mean elastic modulus from MSSER was closer in value to themean Enduratec measurement than the value obtained from SWEI, allelastic modulus values overlapped in standard deviation. The variance inelastic modulus values reported in Table III was much larger than thevariance reported in Table II and was a result of the more inhomogeneouscomposition of the pig tissue structure. As shown in the B-mode image inFIG. 11A, there appeared to be thin fibrous structures that randiagonally across homogeneous muscle tissue, which are located byarrows. These structures became more apparent in the conventional ARFIimages in FIGS. 11B and C for peak displacement and time to 67%recovery. Using the parametric data from SWEI, it was possible to fitMSSER displacement data to the Standard Linear model, and Equations (9)and (14) were used to solve for all mechanical components of the modelalong with force magnitude. These parametric images in FIGS. 11D-Ishowed the same delineation of thin fibrous structures from thesurrounding muscular tissue (arrows). As predicted, the values of forcemagnitude shown in FIG. 11D are much larger than the values depicted inthe gelatin phantoms due to a much larger attenuation. Local areas ofhigher force magnitude [shown as bright areas in FIG. 11D] may be theresult of focused acoustic radiation force at 20 mm and local areas ofincreased attenuation and/or decreased speed of sound. This areacorresponded with the thin fibrous structure in other parametric images.With the exception of the parametric image for μ₀ in FIG. 11G, imagesdisplaying other Standard Linear parameters showed additionaldelineation of tissue structure that was not apparent from conventionalARFI images.

The presently disclosed subject matter presents a fully quantitativemethod for acoustic radiation-force imaging by taking advantage ofdiscrete viscoelastic models to exploit tissue mechanical properties.Previous works in this area of research have generally involved twodifferent approaches to modeling the mechanical response of tissue toacoustic radiation force. Finite element models based on weak-formelastodynamics [30], [31], [37] have been employed to providecomprehensive models of tissue response in three dimensions. Althoughthese models neglect force dissipation, they offer the primary advantageof taking shear wave propagation and the interconnection of tissueelements into account. By modeling force distribution in threedimensions, finite element models can account for the load placed on avolume of tissue rather than a single point of interest. Although thediscrete models used herein explain the relaxation of tissue throughviscoelastic creep, it is likely that there is an “apparent” relaxationof tissue due to finite propagation speeds of shear waves. Althoughdiscrete viscoelastic approaches neglect these effects, they offerreadily realizable equations and computational efficiency, and they takeinto account the dissipation of force by offering a viscous component tothe model.

CONCLUSIONS

The systems and methods presented herein attempt to solve fully for allparameters characterizing viscoelastic tissue response to acousticradiation force. The beam sequences can mimic a materials creep test,which can be referred to as mechanical steady-state excitation andrecovery imaging (MSSER). When applied force magnitude was known throughexperimental characterization of the imaging system, estimates ofelastic modulus values were obtained from gelatin tissue phantoms andpig muscle. Results were in agreement with values obtained frommechanical testing of the samples, which supports the principle that theapproximation of MSSER imaging as uniaxial mechanical compression isvalid in the experimental context. With force magnitude consideredunknown but elastic modulus data provided through SWEI, parametricimages of mechanical parameters can be rendered. Results can generallybe expected to improve with higher intensity pushing forces in morecompliant tissue, higher tissue echogenicity, and more homogeneoustissue samples. Estimates of elastic modulus can be expected to sufferwhen MSSER imaging is singly applied to inhomogeneous tissue samplesbecause it is unable to detect local changes in attenuation and speed ofsound for force magnitude estimations.

However, when elastic modulus data are provided through a combinedimaging approach with SWEI, quantitative results from MSSER CaO beexpected to perform well in viscoelastic, echogenic tissue samples,independent of applied radiation force magnitude. From the resultspresented hereinabove, it is apparent that MSSER can provide valuableinformation about the mechanical properties of tissue that are notobtained in previously described radiation force imaging techniques.

Exemplary Hardware and Software Implementation

As stated above in the Methods section, the subject matter describedherein can be implemented using a commercially available scannerequipped with a transducer and a computer programmed to perform themechanical property parameter value estimations described herein. FIG.12 is a block diagram of an exemplary system for determining mechanicalproperties of a sample according to an embodiment of the subject matterdescribed herein. Referring to FIG. 12, the system includes an acousticmonitor 1200 and an acoustic transducer 1202 for applying acousticenergy to a sample 1204 to apply mechanical force to the sample and formeasuring displacements of the sample resulting from the application ofthe acoustic energy and timings of the displacements. In one example,acoustic monitor 1200 and acoustic transducer 1202 can be implementedusing the above-described ultrasound scanner and linear arraytransducer. Sample 1204 can be any material for which mechanicalproperties are desired to be determined, whose response to applied forcecan be modeled using a mechanical model, and whose displacement inresponse to the applied force can settle to an equilibrium value. Forexample, sample 1204 may be a biological tissue sample, such as a humantissue sample, or a non-biological sample, such as a textile materialsample. In addition, although the term “sample” is used herein todescribe the viscoelastic material being tested, this term is intendedto include both in vivo and ex vivo biological materials.

In FIG. 12, the system further includes a mechanical propertiesestimator 1206 for using a mechanical model to model a mechanicalresponse of the sample to applied force. The model may model a steadystate response of the sample during application of the acoustic energyand a recovery response that occurs after cessation of the applicationof the acoustic energy. Mechanical properties estimator 1206 maydetermine quantitative values of mechanical property parameters of themodel using the displacements and the timings of the displacements(illustrated as RF data in FIG. 12. For example, mechanical propertiesestimator 1206 may estimate the elastic modulus of sample 1204 usingeither of the techniques described above. Mechanical propertiesestimator 1206 may use the estimated elastic modulus and determine theapplied force magnitude using Equations (9) and (14) described above.Mechanical properties estimator 1206 may then used the applied forcemagnitude and the monitored displacement values and timings to determinequantitative values for at least one or all of the mechanical propertyparameters in each of the models described above or in other models thatmodel mechanical properties of a system.

In FIG. 12, mechanical properties estimator 1206 is shown as beingseparate from acoustic transducer 1202. However, the subject matterdescribed herein is not limited to such an implementation. In analternate implementation, mechanical properties estimator 1206 may beintegrated within an acoustic scanner, such as an ultrasound scanner.

FIG. 13 is a flow chart illustrating an exemplary process that may beimplemented by mechanical properties estimator 1206 to determinemechanical properties of a sample using received RF data according to anembodiment of the subject matter described herein. Referring to FIG. 13,in step 1300, radio frequency data resulting from application ofacoustic energy to a sample is received. The radio frequency dataincludes displacements of the sample caused by the application of theacoustic energy and timings of the displacements. In step 1302, amechanical response of the sample to applied force is modeled using amodel including a plurality of mechanical property parameters, whereinthe model models a steady state response of the sample duringapplication of the acoustic energy and a recovery response that occursafter cessation of the application of the acoustic energy. For example,mechanical properties estimator 1206 may use any mechanical model, suchas the Voigt or standard linear model described above, to model behaviorof the system. In step 1304, a quantitative value is determined for atleast one of the parameters using the model, the displacements, and thetimings of the displacements. For example, mechanical propertiesestimator 1206 may estimate the elastic modulus of the sample using anyof the techniques described above, calculate the applied force magnitudeusing Equations (9) and (14), and determine quantitative values for theparameters in the model using the applied force magnitude and thedisplacement and time values.

Applications

The subject matter described herein for determining mechanicalproperties of materials may be used for diagnostic medical applications,non-diagnostic basic science applications, and non-medical,non-basic-science applications. Examples of diagnostic medicalapplications include tissue differentiation based on differences inmechanical properties, monitoring disease progression or response totherapeutic treatment based on changes in mechanical properties oftissue over time in response to disease progression or therapeutictreatment, etc.

By way of specific example, MSSER imaging as described herein can beused to detect atherosclerotic plaques and describe their compositionand structure. In this manner, MSSER can improve cardiovascular riskassessment and support proper administration of therapeuticinterventions, including drug therapies and/or procedures. MSSER imagingcan also be used to detect malignant tumors and distinguish them frombenign lesions. MSSER is also relevant to describing tumor size, shape,structure, and composition, and the systems, methods, and computerreadable media described herein can be implemented to monitor responseto therapy or progression over time (i.e. changes in tumor size, shape,or composition). Similarly, MSSER imaging can be used to detect changesin liver tissue composition consistent with cirrhosis, cancer, or otherdiseases. In addition, MSSER imaging can be used to monitor transplantkidney status, predict causes of graft failure, and detect andcharacterize kidney disease in native kidneys. In yet another example,MSSER can be used to assess the mechanical properties of muscle inregard to monitoring musculoskeletal diseases such as Duchenne musculardystrophy and to establishing the efficacy of treatments. MSSER cansimilarly be applied to monitor changes in muscular propertiesassociated with physical or drug therapies, or to changes in themechanical properties of tendons, ligaments, or bones. In still anotherexample, MSSER imaging can be used to monitor ablation procedures inregard to defining the location and size of the ablated tissue region.

Further, an example of a non-diagnostic basic science application forwhich the subject matter described herein can be used is non-destructivetesting of the mechanical properties of engineered tissue. For instance,MSSER imaging can be used to measure the mechanical properties ofengineered tissues to assess the impact of various environmentalfactors, including chemical, thermal, electrical, magnetic, andmechanical environments. Engineered tissue can be formed by subjectingstem cells to environmental conditions that cause the stem cells todifferentiate into bone cells, nerve cells, muscle cells, etc. Currenttechniques for testing the mechanical properties of engineered tissuesamples are destructive, preventing successive tests involving the samesample and requiring destruction of multiple samples to determinemechanical properties of samples at different stages of tissuedifferentiation. Because the techniques described herein can determinethe mechanical properties of tissue non-destructively, plural tests canbe performed for the same sample to test the mechanical properties ofthat sample. As a result, the same engineered tissue sample can berepeatedly used to determine how the mechanical properties of engineeredtissue change over time or in response to a sequence of differentmechanical tests.

In another example, MSSER imaging can be implemented to assess themechanical properties of excised tissue samples, both human and animal,for mechanical property assessment to delineate disease pathophysiology,natural history, response to therapy, etc. Again, because MSSER is anon-destructive approach, the same sample may be examined serially byMSSER imaging.

Examples of non-medical, non-basic-science samples that can be testedusing the subject matter described herein include any materials forwhich it is desirable to non-destructively determine its mechanicalproperties. Specifically, for example, MSSER can be used tonondestructively test the mechanical properties of textiles, rubbers,polymers, and other non-biological materials.

As stated above, the subject matter described herein may be used todetermine mechanical properties of viscoelastic and other types ofmaterials, such as purely elastic materials whose mechanical behavior inresponse to applied mechanical force can be accurately modeled using amechanical model that models a mechanical response of the material whenexcited by a forcing function and whose displacement can settle to anequilibrium value under application of the forcing function. In order todetermine the mechanical properties of purely elastic materials, itwould be necessary to model the mechanical behavior of such materials inresponse to applied mechanical force using a mathematical model. MSSERwould then be used to apply mechanical force to the materials usingacoustic energy. The resulting displacements and timings of thedisplacements would then be recorded. From the displacements and timingsof the displacements, quantitative values for the parameters in themodel could be determined.

For non-viscous elastic materials, an elastic model may be used. Theterm “elastic model” varies greatly across the literature. It can be assimple as a phenomenological experimental approach such as taking theinstantaneous slope of the measured/applied force versus displacementresponse, and calling this slope a “modulus”. At the other end of thespectrum, more elaborate finite element method (FEM) simulations areconducted on the domain with boundary conditions that model the specificexperimental loading set-up. The resulting numerical simulations thengenerate a force-displacement curve that is curve-fit to the measuredexperimental force-displacement response, thus yielding the material'sintrinsic elastic properties (e.g. Young's modulus, Poisson's ratio forlinear isotropic elasticity) via optimization.

Of course, it is to be understood that the examples listed are but asmall sampling of the many uses for the systems, methods, and computerreadable media described herein. In this regard, the examples listedabove are intended to be representative of the types of applications forthe disclosed technology and not limiting.

REFERENCES

The disclosure of each of the references listed below is herebyincorporated herein by reference in its entirety.

-   1. J. F. Greenleaf, M. Fatemi, and M. Insana, “Selected methods for    imaging elastic properties of biological tissues,” Annu. Rev.    Biomed. Eng., vol. 5, pp. 57-78, 2003.-   2. A. Samani and D. Plewes, “An inverse problem solution for    measuring the elastic modulus of intact ex vivo breast tissue    tumours,” Phys. Med. Biol., vol. 52, no. 5, pp. 1247-1260, 2007.-   3. M. Bilgen and M. F. Insana, “Elastostatics of a spherical    inclusion in homogeneous biological media,” Phys. Med. Biol., vol.    43, no. 1, pp. 1467-1473, 2002.-   4. T. Varghese, J. Zagzebski, and F. Lee, “Elastographic imaging of    thermal lesions in the liver in vivo following radiofrequency    ablation: Preliminary results,” Ultrasound Med. Biol., vol. 28, pp.    1467-1473, 2002.-   5. M. Sridhar, J. Liu, and M. F. Insana, “Viscoelasticity imaging    using ultrasound: Parameters and error analysis,” Phys. Med. Biol.,    vol. 52, pp. 2425-2443, 2007.-   6. J. Ophir, S. K. Alam, B. Garra, F. Kallel, E. Konofagou, T.    Krouskop, and T. Varghese, “Elastography: Ultrasonic estimation and    imaging of the elastic properties of tissue,” in Proc. Inst. Mech.    Eng. [H], vol. 213, 1999, pp. 203-233.-   7. D. Fu, S. Levinson, S. Gracewski, and K. Parker, “Noninvasive    quantitative reconstruction of tissue elasticity using an iterative    forward approach,” Phys. Med. Biol., vol. 45, no. 6, pp. 1495-1509,    2000.-   8. D. Plewes, J. Bishop, A. Samani, and J. Sciarretta,    “Visualization and quantification of breast cancer biomechanical    properties with magnetic resonance elastography,” Phys. Med. Biol.,    vol. 45, no. 1, pp. 1591 1610, 2000.-   9. R. Sinkus, J. Lorenzen, D. Schrader, M. Lorenzen, M. Dargatz,    and D. Holz, “High-resolution tensor MR elastography for breast    tumor detection,” Phys. Med. Biol., vol. 45, no. 6, pp. 1649-1664,    2000.-   10. D. Steele, T. Chenevert, A. Skovoroda, and S. Emelianov,    “Three-dimensional static displacement, stimulated echo NMR    elasticity imaging,” Phys. Med. Biol., vol. 45, no. 1, pp.    1633-1648, 2000.-   11. S. Park, S. R. Aglyamov, W. G. Scott, and S. Y. Emelianov,    “Strain imaging using conventional and ultrafast ultrasound imaging:    Numerical analysis,” IEEE Trans. Ultrason., Ferroelect., Freq.    Contr., vol. 54, no. 5, pp. 987-995, 2007.-   12. L. Taylor, B. Porter, D. Rubens, and K. Parker,    “Three-dimensional sonoelastography: Principles and practices,”    Phys. Med. Biol., vol. 45, pp. 1477-1494, 2000.-   13. E. W. Van Houten, J. B. Weaver, M. I. Miga, F. E. Kennedy,    and K. D. Paulsen, “Elasticity reconstruction from experimental MR    displacement data: Initial experience with an overlapping subzone    finite element inversion process,” Med. Phys., vol. 27, no. 1, pp.    101-107, 2000.-   14. T. E. Oliphant, A. Manduca, R. L. Ehman, and J. F. Greenleaf,    “Complex-valued stiffness reconstruction from magnetic resonance    elastography by algebraic inversion of the differential equation,”    Magn. Reson. Med., vol. 45, pp. 299-310, 2001.-   15. A. L. McKnight, J. L. Kugel, P. J. Rossman, A. Manduca, L. C.    Hartmann, and R. L. Ehman, “MR elastography of breast cancer:    Preliminary results,” AJR Am. J. Roentgenol., vol. 178, no. 6, pp.    1411-1417, 2002.-   16. T. J. Hall, Y. N. Zhu, and C. S. Spalding, “In vivo real-time    freehand palpation imaging,” Ultrasound Med. Biol., vol. 29, no. 3,    pp. 427-435, 2003.-   17. R. A. Baldewsing, F. Mastik, J. A. Schaar, P. W. Serruys,    and A. F. W. van der Steen, “Young's modulus reconstruction of    vulnerable atherosclerotic plaque components using deformable    curves,” Ultrasound Med. Biol., vol. 32, no. 2, pp. 201-210, 2006.-   18. R. A. Baldewsing, J. A. Schaar, F. Mastik, and A. F. van der    Steen, “Local elasticity imaging of vulnerable atherosclerotic    coronary plaques,” Adv. Cardiol., vol. 44, pp. 35-61, 2007.-   19. R. L. Maurice, M. Daronat, J. Ohayon, E. Stoyanova, F. S.    Foster, and G. Cloutier, “Non-invasive high-frequency vascular    ultrasound elastography,” Phys. Med. Biol., vol. 50, pp. 1611-1628,    2005.-   20. M. Fatemi and J. Greenleaf, “Ultrasound-stimulated vibroacoustic    spectrography,” Science, vol. 280, pp. 82-85, 1998.-   21. A. Sarvazyan, O. Rudenko, S. Swanson, J. Fowlkes, and S.    Emelianov, “Shear wave elasticity imaging: A new ultrasonic    technology of medical diagnostics,” Ultrasound Med. Biol., vol. 24,    no. 9, pp. 1419-1435, 1998.-   22. W. F. Walker, F. J. Fernandez, and L. A. Negron, “A method of    imaging viscoelastic parameters with acoustic radiation force,”    Phys. Med. Biol., vol. 45, no. 6, pp. 1437-1447, 2000.-   23. F. Viola and W. F. Walker, “Radiation force imaging of    viscoelastic properties with reduced artifacts,” IEEE Trans.    Ultrason., Ferroelect, Freq. Contr., vol. 50, no. 6, pp. 736-742,    2003.-   24. E. Konofagou, J. Thierman, and K. Hynynen, “A focused ultrasound    method for simultaneous diagnostic and therapeutic applications—A    simulation study,” Phys. Med. Biol., vol. 46, no. 11, pp. 2967-2984,    2001.-   25. K. Nightingale, R. Bentley, and G. E. Trahey, “Observations of    tissue response to acoustic radiation force: Opportunities for    imaging,” Ultrason. Imag., vol. 24, pp. 100-108, 2002.-   26. J. Bercoff, M. Tanter, and M. Fink, “Supersonic shear imaging: A    new technique for soft tissue elasticity mapping,” IEEE Trans.    Ultrason., Ferroelect, Freq. Contr., vol. 51, no. 4, pp. 396-409,    2004.-   27. K. Nightingale, M. Soo, R. Nightingale, and G. Trahey, “Acoustic    radiation force impulse imaging: In vivo demonstration of clinical    feasibility,” Ultrasound Med. Biol., vol. 28, no. 2, pp. 227-235,    2002.-   28. K. Nightingale, S. McAleavey, and G. Trahey, “Shear wave    generation using acoustic radiation force: In vivo and ex vivo    results,”Ultrasound Med. Biol., vol. 29, no. 12, pp. 1715-1723,    2003.-   29. G. E. Trahey, M. L. Palmeri, R. C. Bentley, and K. R.    Nightingale, “Acoustic radiation force impulse imaging of the    mechanical properties of arteries: In vivo and ex vivo results,”    Ultrasound Med. Biol., vol. 30, no. 9, pp. 1163-1171, 2004.-   30. M. L. Palmeri, S. A. McAleavey, K. L. Fong, G. E. Trahey,    and K. R. Nightingale, “Dynamic mechanical response of elastic    spherical inclusions to impulsive acoustic radiation force    excitation,” IEEE Trans. Ultrason., Ferroelect, Freq. Contr., vol.    53, no. 11, pp. 2065-2079, 2006.-   31. M. L. Palmeri, A. C. Sharma, R. R. Bouchard, R. W. Nightingale,    and K. R. Nightingale, “A finite-element method model of soft tissue    response to impulsive acoustic radiation force,” IEEE Trans.    Ultrason., Ferroelect, Freq. Contr., vol. 52, no. 10, pp. 1699-1712,    2005.-   32. K. R. Nightingale, L. Zhai, J. J. Dahl, K. D. Frinkley,    and M. L. Palmeri, “Shear wave velocity estimation using acoustic    radiation force impulsive excitation in liver in vivo,” in Proc.    IEEE Ultrason. Symp., vol. 1, 2006, pp. 1156-1160.-   33. Y. C. Fung, Biomechanics: Mechanical Properties of Living    Tissues. 2nd ed. New York: Springer, 1993.-   34. W. Nyborg, “Acoustic streaming,” in Physical Acoustics. vol.    IIB, W. Mason, Ed. New York: Academic, 1965, ch. 11, pp. 265-331.-   35. E. L. Madsen, J. A. Zagzebski, R. A. Banjavie, and R. E. Jutila,    “Tissue mimicking materials for ultrasound phantoms,” Med. Phys.,    vol. 5, no. 5, pp. 391-394, 1978.-   36. M. F. Insana, J. A. Zagzebski, and E. L. Madsen, “Acoustic    backscattering from ultrasonically tissuelike media,” Med. Phys.,    vol. 9, no. 6, pp. 848-855, 1982.-   37. M. L. Palmeri, S. A. McAleavey, G. E. Trahey, and K. R.    Nightingale, “Ultrasonic tracking of acoustic radiation    force-induced displacements in homogeneous media,” IEEE Trans.    Ultrason., Ferroelect., Freq. Contr., vol. 53, no. 7, pp. 1300-1313,    2006.-   38. “Exposure criteria for medical diagnostic ultrasound: II.    Criteria based on all known mechanisms,” National Council on    Radiation Protection and Measurements, Bethesda, Md., NCRP    Publications, Report No. 140, 2002.

The present subject matter can be embodied in other forms withoutdeparture from the spirit and essential characteristics thereof. Theembodiments described therefore are to be considered in all respects asillustrative and not restrictive. Although the present subject matterhas been described in terms of certain preferred embodiments, otherembodiments that are apparent to those of ordinary skill in the art arealso within the scope of the present subject matter.

1. A method for determining values for mechanical property parameters ofa sample, comprising: applying acoustic energy to a sample to apply amechanical force to the sample; measuring a response by the sampleduring the application of the acoustic energy to determine a value for afirst mechanical property parameter of the sample; measuring a recoveryresponse of the sample following cessation of the application of theacoustic energy to determine a value for at least one second mechanicalproperty parameter of the sample; and determining a value for at leastone additional mechanical property parameter of the sample based on amathematical relationship between the first, at least one second, and atleast one additional mechanical property parameters.
 2. The method ofclaim 1 wherein the sample comprises a viscoelastic sample.
 3. Themethod of claim 1 wherein applying acoustic energy to a sample comprisesapplying acoustic energy to a biological tissue sample.
 4. The method ofclaim 1 wherein the first mechanical property parameter is an elasticmodulus of the sample.
 5. The method of claim 1 wherein the at least onesecond mechanical property parameter comprises a relaxation timeconstant for constant stress of the sample.
 6. The method of claim 1wherein determining a value for at least one additional mechanicalproperty parameter comprises applying one of a Voigt model or a standardlinear model.
 7. The method of claim 6 wherein the first mechanicalproperty parameter comprises an elastic modulus of the sample; whereinthe at least one second mechanical property parameter comprises arelaxation time constant for constant stress; wherein mathematicalrelationship comprises the Voigt model; and wherein the at least oneadditional mechanical property parameter comprises a spring constant ofa spring in the Voigt model and a coefficient of viscosity of a dashpotin the Voigt model.
 8. The method of claim 6 wherein the firstmechanical property parameter comprises an elastic modulus of thesample; wherein the at least one second mechanical property comprises arelaxation time constant for constant strain and a relaxation timeconstant for constant stress; wherein the mathematical relationshipcomprises the standard linear model; and wherein the at least oneadditional parameter comprises a spring constant of a first spring inthe standard linear model, a spring constant of a second spring in thestandard linear model, and a coefficient of viscosity of a dashpot inthe standard linear model.
 9. The method of claim 1 comprisingdetermining an applied force magnitude received by the sample based on amathematical relationship between the first, the at least one second,and the at least one additional mechanical property parameters and theapplied force magnitude received by the sample.
 10. The method of claim9 comprising determining one or more of an absorption coefficient of thesample or a speed of sound through the sample based on knownmathematical relationships between the force magnitude, the absorptioncoefficient of the sample, and the speed of sound through the sample.11. The method of claim 1 comprising using the values determined for themechanical property parameters for a diagnostic medical purpose.
 12. Themethod of claim 1 comprising using the values determined for themechanical property parameters for a non-diagnostic basic sciencepurpose.
 13. The method of claim 12 wherein the sample comprisesengineered tissue and wherein the non-diagnostic basic science purposeincludes identifying mechanical properties of the engineered tissue. 14.The method of claim 1 comprising using the values determined for themechanical property parameters for a non-medical purpose.
 15. A methodfor quantifying at least one mechanical property parameter of a sample,the method comprising: applying acoustic energy to a sample to applymechanical force to the sample and measuring resulting displacements ofthe sample and timings of the displacements; modeling mechanicalproperties of the sample using a mathematical model of a mechanicalresponse of the sample to applied force, wherein the model includesparameters for the mechanical properties of the sample and wherein themodel models a steady state response of the sample during application ofthe acoustic energy and a recovery response that occurs after cessationof the application of the acoustic energy; and determining, using themodel, the measured displacements, and the measured timings, aquantitative value for at least one of the parameters in the model. 16.The method of claim 15 wherein the sample comprises a viscoelasticsample.
 17. The method of claim 16 wherein determining a quantitativevalue for at least one of the parameters includes determining aquantitative value for at least one of: an elastic modulus, a springconstant, a coefficient of viscosity, a relaxation time constant forconstant strain, and a relaxation time constant for constant stress. 18.The method of claim 15 wherein determining a quantitative value for atleast one of the parameters comprises: estimating an elastic modulus ofthe sample using timing and displacement data measured from locationslateral to a region of acoustic radiation excitation of the sample;estimating an applied acoustic radiation force magnitude from theelastic modulus and timing and displacement data measured from positionswithin the region of radiation excitation of the sample; and computingthe values for the parameters in the model using the estimated appliedacoustic radiation force magnitude.
 19. The method of claim 15comprising determining an applied acoustic radiation force magnitude bycalculating a body force magnitude using measured parameter values fromthe sample or from a material having a similar composition as the sampleand multiplying the body force magnitude by dimensions over which theacoustic energy is applied.
 20. The method of claim 15 comprisingdetermining an applied acoustic radiation force magnitude by measuringan elastic modulus of the sample and estimating the applied acousticradiation force magnitude using a relationship between the elasticmodulus, a correction factor, and dimensions over which the acousticenergy is applied.
 21. The method of claim 15 wherein applying theacoustic energy includes applying the acoustic energy in a manner thatsimulates a mechanical creep test.
 22. A system for determining at leastone mechanical property of a sample, the system comprising: an acousticmonitor and an acoustic transducer for applying acoustic energy to asample to apply mechanical force to the sample and for measuringdisplacements of the sample resulting from the application of theacoustic energy and timings of the displacements; and a mechanicalproperties estimator for using a model to model a mechanical response ofthe sample to applied force, wherein the model models a steady stateresponse of the sample during application of the acoustic energy and arecovery response that occurs after cessation of the application of theacoustic energy, and for determining a quantitative value for at leastone of the mechanical property parameters of the model using thedisplacements and the timings of the displacements.
 23. The system ofclaim 22 wherein the sample comprises a viscoelastic sample.
 24. Thesystem of claim 23 wherein the mechanical properties estimator isconfigured to determine a quantitative value for at least one of: anelastic modulus, a spring constant, a coefficient of viscosity, arelaxation time constant for constant strain, and a relaxation timeconstant for constant stress.
 25. The system of claim 22 wherein theacoustic transducer is configured to apply pulses of acoustic energy tothe sample for a time period and to measure a response of the sampleduring the application of the pulses and a recovery response followingthe application of the pulses.
 26. The system of claim 23 wherein themechanical properties estimator is configured to determine an elasticmodulus of the sample and to estimate values for at least one additionalmechanical property parameter of the sample based on the elasticmodulus.
 27. The system of claim 26 wherein the mechanical propertiesestimator is configured to apply a standard linear model; and whereinthe at least one additional parameter comprises a relaxation timeconstant for constant stress, a relaxation time constant for constantstrain, a spring constant for a first spring in the model, a springconstant for a second spring in the model, and a coefficient ofviscosity for a dashpot in the model.
 28. The system of claim 26 whereinthe mechanical properties estimator is configured to apply a Voigtmodel; and wherein the at least one additional parameter includes arelaxation time constant for constant stress, a spring constant for aspring in the model, and a coefficient of viscosity for a dashpot in themodel.
 29. The system of claim 22 wherein the acoustic transducer isconfigured to apply acoustic energy in a manner that simulates amechanical creep test of the sample.
 30. The system of claim 22 whereinthe mechanical properties estimator is configured to determine amagnitude of acoustic radiation force applied to the sample.
 31. Acomputer readable medium having stored thereon executable instructionsthat when executed by the processor of a computer control the computerto perform steps comprising: receiving radio frequency data resultingfrom application of acoustic energy to a sample, the radio frequencydata including displacements of the sample resulting from application ofthe acoustic energy and timings of the displacements; modeling amechanical response of the sample to applied force using a modelincluding a plurality of mechanical property parameters, wherein themodel models a steady state response of the sample during application ofthe acoustic energy and a recovery response that occurs after cessationof the application of the acoustic energy; and determining aquantitative value for at least one of the parameters using the model,the displacements, and the timings of the displacements.